Intersections of perfect binary codes

• Intersections of perfect binary codes are investigated. In 1998 Etzion and Vardy proved that the intersection number η(C;D), for any two distinct perfect codes C and D, is always in the range 0 ≤η(C;D) ≤2 n-log(n+1)-2(n-1)/2; where the upper bound is attainable. We improve the upper bound and show that the intersection number 2n-log(n+1) -2(n-1)/2 is "sporadic". We also find a large class of intersection numbers for perfect binary codes of length 15 and for any admissible n >15 a new set of intersection numbers for perfect codes of length n.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Data- och informationsvetenskap -- Annan data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Other Computer and Information Science (hsv//eng)

Nyckelord

Intersection number

Large class

Perfect codes

Upper Bound

Electronics engineering

Binary codes

Publikations- och innehållstyp

ref (ämneskategori)

kon (ämneskategori)